From a group of 7 batsmen and 6 bowlers, 10 players are to be chosen for a team, which should include atleast 4 batsmen and atleast 4 bowlers. One batsmen and one bowler who are captain and vice-capta

Question

From a group of 7 batsmen and 6 bowlers, 10 players are to be chosen for a team, which should include atleast 4 batsmen and atleast 4 bowlers. One batsmen and one bowler who are captain and vice-captain respectively of the team should be included. Then the total number of ways such a selection can be made, is

TestHub · Accepted Answer

7 Batsmen \& 6 Bowlers
To select 10 players including atleast
4 Batsmen \& 4 Bowlers
Captain \& vice-captain already selected
$No. of ways =^{6} C_{5} \times^{5} C_{3} +^{6} C_{4} \times^{5} C_{4} +^{6} C_{3} \times^{5} C_{5} = 6 \times 10 + 15 \times 5 + 20 \times 1 = 60 + 75 + 20 = 155$

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